5

Ints) . Compute the intervals of increasing and decreasing for the function f(c) = 1+12...

Question

Ints) . Compute the intervals of increasing and decreasing for the function f(c) = 1+12

ints) . Compute the intervals of increasing and decreasing for the function f(c) = 1+12



Answers

Find the approximate intervals on which the function is increasing, those on which it is decreasing, and those on which it is constant. $$f(x)=\frac{1}{x}$$

It's on the interval. The Christian on it from here on the way to here. And we corresponded about off minus three and three here so they found and decreasing. We'll be on the interval from ministry to three and arrest interval will be increasing so increasing well beyond interval vermin. Infinity two months three Union the interval from Ridge infinity.

I have a function of co sign swear X on the interval, negative pi to pie, and I'm trying to determine where the function increases in decreases. I am going to rewrite the coastline squared X so that the derivatives a little bit easier to take by putting the square term outside of a parentheses. Let's find our critical points. The derivative function is going to use the chain world power out front. Subtract one from the old power. So that's the first multiplied by the derivative of the inside, which is negative. Sign axe and bringing the negative OutFront gives me negative to co sign X sine X Critical points are going to occur any time that derivative is equal to zero. That is true. Any time co sign x zero or sine x zero coastline x zero on the interval. Negative pie to positive pie at the angles of negative pi over two and positive pi over two sign axes equals zero on the negative pie. The pie interval Atnegative pie zero and positive pot. Now I would put those in order on a number line from smallest angle the largest. So we go negative pie. Negative pi over two zero pi over two in pot. Those all give us derivatives of zero. Let's check the sign of the derivative on angles between them. So if I filled in an England here like negative three pi over four, I would get a derivative. That is a negative times. A negative times a negative negative answer. Phil. Angolan in here like negative pi over four. I would have a negative time, the positive times a negative. That's positive. Fill in the angle pi over four and I would have a negative time to positive times. A positive that's negative. And finally Fillon angle in like three pi over four and I would have a negative times a negative times a positive, so positive again. So we're looking at a decreasing region, the increasing a decreasing and once again an increase. So the function decreases from negative pie to negative pi over two as well as zero to positive pi over two. It increases from negative pi over 2 to 0 as well as pi over two two pi

In this question we have to find the interval of increasing and decreasing for the function that is effects. It was too into the power X. For sex. And we have to take the interval affects that starts with zero and and set to buy. Okay, so to calculate or to find the into all of increasing or decreasing function. We have to start with the delivery to So here I am going to find that deliver to of effects. Okay. Means that the checks and we have to calculate it Byproduct able since that is productive two functions. So I can say that it was the products remains as it is and derivative of course after that course as it is and deliver developed between the power X. Okay. No, we can say that derivative of course is minus Sine X less. Cossacks into derivative. Into the public. Access to the public. If I take care of to the vortex common then I get here Cossacks minus Synnex. Okay, this is the value of derivative which you should get now to find the in develop increasing and decreasing. I have to Put this derivative equals to zero. I put it. It was 20. Okay, if I go to the studio then I get into the Power X. Into Cossacks minus sine X equals to zero. If we divide by two, the power X, then we get here Cossacks minus Sine X equals €2. Main score. Sex. It was to Synnex if we divide by Cossacks then we get to annex it was 21 And what are they given interval? We know that the value of the next equals to one arises when exceeds by by four or five by by four. Okay, It arises their toxic was too by by four or 5 by by four. So these are the values of political points. I can say that these are the critical points. Now I'm going to lower the number line for these points. Okay, I'm going to plot on a number line. So I am going to make a number line here for the given interval. The given interval starts with zero and answered to pie. And in them between there are paid by foreign Fight by by four. Okay. And we know that our derivative was a dash X equals two. It was the Power X. Cossacks minus Sine X. Now we have to take the sign representation here is the total value From the interval of 02 by by four. Then this derivative shows a positive sign. And if we take a value in there and developed by by foreign bible too, then it shows a negative value and in the third part also it shows a positive value. Okay now we have to calculate the order of increasing so I know that our function is in increasing function. Okay. If they're derivative remains was too if delivered you remain supposed to and from the about number nine you can calculate the interval. You can see where the derivative is cost if it is in the in developed zero to pi by four And after that the union 5554 to buy. Okay. Similarly we have to find the order of decreasing. So do find the in developed the grazing. I can say that Derivatives should be less than zero. And here you can see that your derivative is less than bureau In the interval of by by 4: five by by four. Okay. So the function is decreasing in the in developed 5542 five x by four. So these are my answers means Increasing into Elise didn't do by by four and the union of Bye Bye 45 by by 4 to 2 pi. And in develop, decreasing is Bye Bye 4 to fight by my foot. Okay, thank.

Have a little bit more complicated function here. X square, natural log, X squared plus one. And we're told that we want to find where we have increasing and decreasing regions. I have written off a little bit of a note here we are not allowed to take the natural log of zero, and the natural log of zero would occur if x zero so X is excluded from our domain. To find our critical points, we will first take the derivative. So we're going to the product rule on the X squared natural log X word part. That would be first times the derivative of the second, the derivative. And Ellen, you is do you over you. So that's gonna be X squared on bottom two x on top. That was first derivative of the second plus second derivative of the first, which is two acts and then the derivative of the one at the end of zero. Let's simplify this. The X squared you're gonna cancel. So that's two x plus two X out in X square. Okay, let's solve this. It's never non differential. Accepted the X value of zero, but we already know that that is a discontinuous point. So the critical points are going to come when we set this equal to zero. We can factor out a two x giving us two acts times one plus l A n X squared equals zero. Now that's true. If either the two X is equal to zero or if the l n plus one plus Ln X squared to zero well, to Act zero effect zero. What about this part? Well, that is Onley equal to zero if the natural log of X squared equals negative one. But natural logs cannot equal negative values. So the only critical point of have is X equals zero. Remember what we said In the very beginning, X equals zero wasn't in the domain. So when we check test points, we're gonna put zero down. But we're simply going to say that is a discontinuous point. That is the Onley point, where we could possibly change the sign of the derivative. Let's pick values around that. Let's go with negative one and positive one. If I feel negative one into the derivative function, I would have negative too. Minus two natural log one. What is natural? Look. One natural of one is zero. So really, it's negative two minus zero. So it's negative, too. So it is negative if X is less than negative one. What about the function at positive one? Well, that would give us two plus two. Ellen one and again, Ln one is zero. So we really just have two plus zero. That's two or a positive. So you're looking at the number line. We could say that it is a decreasing function if X is less than zero and an increasing function if X is greater than zero.


Similar Solved Questions

2 answers
(10 points) We consider commodity with daily price changes being independent and iden- tically distributed according to some unknown distribution with mean 0.01 and variance 1/2. Let Co be the price of the commodity today and Cn the price of the commodity in n days Make an asymptotic statement about the probability P[Cn > Co] as n 0 and compute the approximate values for n 50,1000 and 10000_
(10 points) We consider commodity with daily price changes being independent and iden- tically distributed according to some unknown distribution with mean 0.01 and variance 1/2. Let Co be the price of the commodity today and Cn the price of the commodity in n days Make an asymptotic statement abou...
5 answers
Question 6 of 13Attempt 1A current of 5.38 A is passed through a Sn(NO3)2 solution. How long; in hours, would this current have to be applied to plate out 8.20 g of tin?time required: 668
Question 6 of 13 Attempt 1 A current of 5.38 A is passed through a Sn(NO3)2 solution. How long; in hours, would this current have to be applied to plate out 8.20 g of tin? time required: 668...
5 answers
Nebas to Loah Velton Beaele Iesion nethweb(Student Astignment-F Loa h Wndo 0/1 calcuie Find [ points parabola Prevlous = 2 2 -Responses/eubmitzded-218416968t098 6-Loca mith Answers Need E equation "+ ~SCalcET8 3.= Help? 11.075. whose = tangent Show Iina My Work (22) Subril / (Optanel} ( has - Anske equation raclice = Another VersionRatponte
nebas to Loah Velton Beaele Iesion nethweb(Student Astignment-F Loa h Wndo 0/1 calcuie Find [ points parabola Prevlous = 2 2 -Responses/eubmitzded-218416968t098 6-Loca mith Answers Need E equation "+ ~SCalcET8 3.= Help? 11.075. whose = tangent Show Iina My Work (22) Subril / (Optanel} ( has - ...
5 answers
7I0 Dcints DevorestareDetearminecritical value for _ huo-sider Con-ideng intanaeach of the following situations (Rounc Your answerethra? Cecima places )Confidence9596, df =Confidence9590, df = 15Confidence level 9900, df = 15Confoence9900,Confidence evel 9896, dfConfidence9900,
7I0 Dcints Devorestare Detearmine critical value for _ huo-sider Con-ideng intana each of the following situations (Rounc Your answere thra? Cecima places ) Confidence 9596, df = Confidence 9590, df = 15 Confidence level 9900, df = 15 Confoence 9900, Confidence evel 9896, df Confidence 9900,...
5 answers
In which direction is the reaction spontaneous under these conditions?right left
In which direction is the reaction spontaneous under these conditions? right left...
5 answers
Only 45% of registered voters voted in the last election. Will voter participation be even lower for the upcoming election?Ho :Select an answerHa:Select an answer
Only 45% of registered voters voted in the last election. Will voter participation be even lower for the upcoming election? Ho : Select an answer Ha: Select an answer...
5 answers
Conskder Ihe Iinear syslem=6I3The augmented matrx Ior the above Iinear system ISThis has TOW reduced echelon formThe general solution for (his system IS21 T2T31435 21 551612 AI2 10I2AT4 714
Conskder Ihe Iinear syslem =6 I3 The augmented matrx Ior the above Iinear system IS This has TOW reduced echelon form The general solution for (his system IS 21 T2 T3 14 35 21 551 612 AI2 10I2 AT4 714...
5 answers
Ssing = nght17. Consider the following argument:ruining or the sun is in the sky: IS HOI rining; Therefore , the sun is in the sky:(Zpts, )Creale labels for thc simple statements involvedTranslate the argument into symbolic form Use the symbolrepresent therefore: (4pts: )12(6pts )truth table t0 determine if the argument is valid: ConstnuctIs the argument valid?Statement used in truth table:Truth table:
ssing = nght 17. Consider the following argument: ruining or the sun is in the sky: IS HOI rining; Therefore , the sun is in the sky: (Zpts, ) Creale labels for thc simple statements involved Translate the argument into symbolic form Use the symbol represent therefore: (4pts: ) 12 (6pts ) truth tab...
1 answers
The half-life of oxygen-15 is $124 \mathrm{~s}$. If a sample of oxygen-15 has an activity of $4000 \mathrm{~Bq}$, how many minutes will elapse before it reaches an activity of $500 \mathrm{~Bq}$ ?
The half-life of oxygen-15 is $124 \mathrm{~s}$. If a sample of oxygen-15 has an activity of $4000 \mathrm{~Bq}$, how many minutes will elapse before it reaches an activity of $500 \mathrm{~Bq}$ ?...
5 answers
Poni) Anote{ nodetgromth Tuncucn Jr a (Mitco Dobucion Given by thc Compate funceicn wkhsolutkn Io {he dircrential equaion'(#)d Wuncr conbtant and RlIs Itv carrylng apacily Ansuti Ie lolkwina Oueaant; gohethe dlrrontal Gzon Mn aoralant camcmc Dpjory R XKH | ano mllar populatlon R Louo ] AnstttP() io(Inizi"eNa"(0 Ih)Maln €0HK 2u0lmns R IwOltn3 He P(){ Lml m
poni) Anote{ nodet gromth Tuncucn Jr a (Mitco Dobucion Given by thc Compate funceicn wkh solutkn Io {he dircrential equaion '(#)d Wuncr conbtant and RlIs Itv carrylng apacily Ansuti Ie lolkwina Oueaant; gohethe dlrrontal Gzon Mn aoralant camcmc Dpjory R XKH | ano mllar populatlon R Louo ] Anst...
1 answers
Evaluate $\sum_{n=3}^{\infty} 2(1 / 3)^{n}$
Evaluate $\sum_{n=3}^{\infty} 2(1 / 3)^{n}$...
5 answers
A hotel that has 200 rooms sold 110 rooms on Monday, 185 roomson Tuesday, 140 rooms on Wednesday, 165 rooms on Thursday, 110rooms on Friday, 185 rooms on Saturday, and 200 rooms on Sunday.Calculate the occupancy rate.%Round to 2 decimal places
A hotel that has 200 rooms sold 110 rooms on Monday, 185 rooms on Tuesday, 140 rooms on Wednesday, 165 rooms on Thursday, 110 rooms on Friday, 185 rooms on Saturday, and 200 rooms on Sunday. Calculate the occupancy rate. % Round to 2 decimal places...
5 answers
X 28d" 5 Sp Sp Sp 2 Sp Sp'21) 212 1 ) 1 1 1 1nil liwav A i
X 28 d" 5 Sp Sp Sp 2 Sp Sp' 21) 212 1 ) 1 1 1 1 nil liwav A i...
5 answers
Suppose tha: and 3 :re sets guch tbat 4UB={0,1,2,3,4,5,6,7,8 2}, 4-3= {0,3,5,6}, 8 - A={1,4,9}Express A n 2 using the rcster methcd_Express ueing the roster method-Express E using the roster method
Suppose tha: and 3 :re sets guch tbat 4UB={0,1,2,3,4,5,6,7,8 2}, 4-3= {0,3,5,6}, 8 - A={1,4,9} Express A n 2 using the rcster methcd_ Express ueing the roster method- Express E using the roster method...
4 answers
An air conditioner connected to 120 rms ac line is equivalent to 04 9 resistance and 1.72 $ inductive reactance in series_ Calculate (a) the impedance of the air conditioner and (b) the average rate at which energy is supplied to the appliance_(a) NumberUnits(b) NumberUnits
An air conditioner connected to 120 rms ac line is equivalent to 04 9 resistance and 1.72 $ inductive reactance in series_ Calculate (a) the impedance of the air conditioner and (b) the average rate at which energy is supplied to the appliance_ (a) Number Units (b) Number Units...

-- 0.017729--